Power spectral density 2

[WIM32]

To compare measured vibrations with machine specifications, I need to convert acceleration-time signal in to power spectral density. I have FFT equipment available, but I have come up with different definition for PSD. Please help with a correct definition of PSD...
Thanks in advance
Wim

 

[tomirvine]

A PSD can be calculated from an FFT.

The FFT magnitude is squared.

Then multiply by (1/2) to convert G^2 to GRMS^2.

Next, divide by the spectral bandwidth, which is the frequency increment.

The result is a power spectral density in terms of GRMS^2/Hz. Note that by convention this unit is abbreviated as G^2/Hz.

I have posted some tutorials on the power spectral density function at:

http://www.vibrationdata.com

As disclosure, a small fee is required to access the materials at this site.

Sincerely, Tom Irvine

 

[WIM32]

Thanks tomirvine for your quick response, but the strange thing is, that I have found a different definition for RMS value, namely multiply by 1/2*sqrt of 2. How can this be explained, or is this definition for RMS only valid for 1/3rd octave analysis?
Also, is this FFT two sided?
Best regards
wim32

 

[VibrationSpecialist]

Dear wim32,
The Power Spectral Density is simply a method of scaling the frequency of the structure. It is more pronounced for random type of excitation.

 

[WIM32]

VibrationSpecialist,
I indeed measure random vibration, that is why I need to calculate PSD.

 

[VibrationSpecialist]

Dear WIM32,
The instantaneous magnitude of any random vibration are specified only by probability distribution functions giving the probable fraction of the total time that the magnitude lies within specific range.
The Power Spectral Density is really the limiting mean-square value of the random parameter (e.g. acceleration, velocity, displacement, stress, etc.) per unit bandwidth.
As you can see, the PSD is the mean-square (see Tom Irvin message) and not Root Mean Square (RMS). The RMS value of any Sinusoidal Frequency amplitude is equal to the reciprocal of square root of 2 (0.707).
I hope that I am of help to you.
Take Care ;-)

 

Vibration Specialists:

I recently had some PSD data recorded over a very long period of time in real conditions. I need to experimentally test the equipment this data was originally recorded on, but the time period is unreasonable. Is there any way an accurate time experience of less duration can be made by "compressing" the data? Thanks.

 

[tomirvine]

The empirical time scaling formula is:

(W0/W1) = (T1/T0)^(1/M)

where

W0 is the reference level in GRMS
W1 is the new level in GRMS

T0 is the reference time
T1 is the new time

M is the material constant, or slope of log-log S-N curve)

Typically, M=4 is assumed for aerospace vehicles.
(Reference: MIL-STD-1540C).

If you would like further information, I have posted a tutorial on time scaling at:

http://www.vibrationdata.com/tutorials.htm

As disclosure, a small fee is required to access the materials at this site.

Sincerely, Tom Irvine

 

[WIM32]

Hotmetal,

The FFT sampling time (window) is probably not unreasonable long. If you can have the original time data still available, you could decrease the total measuring time to the sampling time width (if this is known). This way your frequency range stays intact. If the processes that are being measured are longer than your sampling time, you should increase the measuring time, so that it always contains complete samples.
Good luck, best regards
Wim32

 

[HOTMETAL]

Thanks Tom, I'll check out the tutorial. Thanks also Wim32. I just have one more question though: is there a limiting value for W1? Or, does this scaling formula only hold for certain ranges of time change? For example, the PSD data was taken over 3200 hours and needs to be compressed into 81 min--won't this give some outrageous values for W1 upon scaling?

 

[HOTWATER]

Thanks Tom, i had the same problem as HOTMETAL and you really helped out a lot

 

Tom,

I checked out the tutorial and I think I have a better handle on how to time scale, but I still have the same question: is there a limiting factor on the empirical time scaling formula? Theoretically, I could scale down the 2000hr data from the tutorial to a 1 second test, but this would not be practical. I realize that some limitations are determined based on equipment. However, assuming that my equipment can generate any new test levels at the appropriate frequencies, how is the largest, reasonable delta between actual time and test time (i.e., the shortest test time) determined?

 

[tomirvine]

There is not an exact answer to your question.

The whole time-scaling method is highly empirical.

For example, the true S-N fatigue curves for the test item materials are seldom, if ever, known.

A further complication is that fatigue is only one of several failure mechanisms. Yielding, Ultimate failure, buckling, and excessive relative displacement are other examples. In addition, some failure modes such as creep are time-dependent.

I thus gave a moderate approach in the tutorial, where a 16 hour per axis test was used to represent 2000 hours of field service.

By the way, the tutorial paper was based on some work that I performed for an actual client.

Unfortunately, the testing project was cancelled due to the client's financial problems.

Sincerely,
Tom Irvine

http://www.vibrationdata.com